Iteration theories: the equational logic of iterative processes
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin u.a.
Springer
1993
|
| Series: | EATCS monographs on theoretical computer science
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 621 - 630 |
| Physical Description: | XV, 630 S. |
| ISBN: | 3540563784 0387563784 |
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Record in the Search Index
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| adam_text | IMAGE 1
S
STEPHEN L. BLOOM ZOLTAEN ESIK
ITERATION THEORIES
THE EQUATIONAL LOGIC OF ITERATIVE PROCESSES
SPRINGER-VERLAG BERLIN HEIDELBERG NEW YORK LONDON PARIS TOKYO HONG KONG
BARCELONA BUDAPEST
IMAGE 2
CONTENTS
PREFACE VII
INTRODUCTION 1
1 MATHEMATICAL MOTIVATION 1
2 WHY ITERATION THEORIES? 4
3 SUGGESTIONS FOR THE IMPATIENT READER 5
4 A DISCLAIMER 6
5 NUMBERING 6
1 PRELIMINARY FACTS 7
1 SETS AND FUNCTIONS 7
2 POSETS 9
3 CATEGORIES 9
4 2-CATEGORIES 15
4.1 CELHJ IS A 2-CATEGORY, TOO 19
5 E-TREES 20
2 VARIETIES AND THEORIES 23
1 E-ALGEBRAS 23
2 TERMS AND EQUATIONS 25
3 THEORIES 29
4 THE THEORY OF A VARIETY. 41
3 THEORY FACTS 47
1 PAIRING AND SEPARATED SUM 47
IMAGE 3
XII CONTENTS
2 ELEMENTARY PROPERTIES OF TH 51
3 THEORIES AS N X N-SORTED ALGEBRAS 53
4 SPECIAL COPRODUCTS 56
5 MATRIX AND MATRICIAL THEORIES 63
5.1 MATRIX THEORIES 63
5.2 THEORIES OF RELATIONS 71
5.3 MATRICIAL THEORIES 72
5.4 SEQUACIOUS RELATIONS 78
5.5 SEQUACIOUS FUNCTIONS 80
6 PULLBACKS AND PUSHOUTS OF BASE MORPHISMS 81
7 2-THEORIES 87
4 ALGEBRAS 93
1 T-ALGEBRAS 93
1.1 AN EXAMPLE: ALGEBRAS OF MATRIX THEORIES 97
2 FREE ALGEBRAS IN T B 100
2.1 THE T-ALGEBRAS T N 100
2.2 INFINITELY GENERATED FREE ALGEBRAS IN T* 103
3 SUBVARIETIES OF 1* 105
4 THE CATEGORIES TH AND VAR 107
5 NOTES 111
5 ITERATIVE THEORIES 113
1 IDEAL THEORIES 113
2 ITERATIVE THEORIES DEFINED 118
3 PROPERTIES OF ITERATION IN ITERATIVE THEORIES 124
4 FREE ITERATIVE THEORIES 140
5 NOTES 157
6 ITERATION THEORIES 159
1 ITERATION THEORIES DEFINED 159
2 OTHER AXIOMATIZATIONS OF ITERATION THEORIES 162
2.1 SCALAR AXIOMATIZATIONS 166
3 THEORIES WITH A FUNCTORIAL DAGGER 175
4 POINTED ITERATIVE THEORIES 184
5 FREE ITERATION THEORIES 191
IMAGE 4
CONTENTS XIII
6 CONSTRUCTIONS ON ITERATION THEORIES 194
7 FEEDBACK THEORIES 204
8 SUMMARY OF THE AXIOMS 210
8.1 AXIOMS FOR ITERATION THEORIES 210
8.2 AXIOMS FOR CONWAY THEORIES 212
9 NOTES 213
7 ITERATION ALGEBRAS 215
1 DEFINITIONS 215
2 FREE ALGEBRAS IN T* 218
3 THE RETRACTION LEMMA 220
4 SOME CATEGORICAL FACTS 222
5 PROPERTIES OF T+ 225
6 A CHARACTERIZATION THEOREM 230
7 STRONG ITERATION ALGEBRAS 235
8 NOTES 241
8 CONTINUOUS THEORIES 243
1 ORDERED ALGEBRAIC THEORIES 243
1.1 FREE ORDERED THEORIES 246
2 W-CONTINUOUS THEORIES 248
2.1 FREE W-CONTINUOUS THEORIES 249
3 RATIONAL THEORIES 254
4 INITIALITY AND ITERATION IN 2-THEORIES 257
5 W-CONTINUOUS 2-THEORIES 273
5.1 THE DEFINITION, WITH EXAMPLES 273
5.2 INITIAL ALGEBRAS EXIST 278
5.3 W-CONTINUOUS 2-THEORIES ARE ITERATION THEORIES 283
6 NOTES 288
9 MATRIX ITERATION THEORIES 289
1 NOTATION 289
2 PROPERTIES OF THE STAR OPERATION 290
3 MATRIX ITERATION THEORIES DEFINED 297
4 PRESENTATIONS IN MATRIX ITERATION THEORIES 313
5 THE INITIAL MATRIX ITERATION THEORY 319
6 AN EXTENSION THEOREM 322
IMAGE 5
XIV CONTENTS
7 MATRIX ITERATION THEORIES OF REGULAER SETS 336
8 NOTES 349
10 MATRICIAL ITERATION THEORIES 353
1 PROM DAGGER TO STAR AND OMEGA, AND BACK 353
2 MATRICIAL ITERATION THEORIES DEFINED 356
3 EXAMPLES 367
3.1 SEQREU 367
3.2 C(X*; R) 370
3.3 KC(X*; X U ) 374
3.4 CC(X*; X ) 374
3.5 KC(X*;X U ) 375
3.6 MORE COMMUTATIVE IDENTITIES 375
4 ADDITIVELY CLOSED SUBITERATION THEORIES 377
4.1 AN A.C. SUBITERATION THEORY OF C(X*; X ) 385
5 PRESENTATIONS IN MATRICIAL ITERATION THEORIES 390
6 THE INITIAL MATRICIAL ITERATION THEORY 395
7 THE EXTENSION THEOREM 399
8 ADDITIVELY CLOSED THEORIES OF REGULAER LANGUAGES 418
9 CLOSED REGULAER W-LANGUAGES 427
10 NOTES 447
11 PRESENTATIONS 449
1 PRESENTATIONS IN ITERATION THEORIES 449
2 SIMULATIONS OF PRESENTATIONS 456
3 COPRODUCTS REVISITED 469
4 NOTES 480
12 FLOWCHART BEHAVIORS 481
1 AXIOMATIZING SEQUACIOUS FUNCTIONS 482
2 AXIOMATIZING PARTIAL FUNCTIONS 485
3 DIAGONAL THEORIES 489
4 SEQUACIOUS FUNCTIONS WITH PREDICATES 494
4.1 THE THEORY OF ONE PREDICATE 494
4.2 SEVERAL BINARY PREDICATES 505
5 PARTIAL FUNCTIONS WITH PREDICATES 508
6 NOTES 511
IMAGE 6
CONTENTS XV
13 SYNCHRONIZATION TREES 513
1 THEORIES OF SYNCHRONIZATION TREES 514
2 GROVE ITERATION THEORIES 521
3 AXIOMATIZING SYNCHRONIZATION TREES 533
4 BISIMILARITY , 540
5 NOTES 549
14 FLOYD-HOARE LOGIC 551
1 GUARDS 552
2 PARTIAL CORRECTNESS ASSERTIONS 562
2.1 AN ALTERNATIVE DEFINITION OF N-GUARDS 564
3 THE STANDARD EXAMPLE 565
4 RULES FOR PARTIAL CORRECTNESS 566
4.1 FORMALIZATION 566
4.2 FORMAL RULES 570
5 SOUNDNESS 571
6 THE STANDARD EXAMPLE, CONTINUED 582
7 A FLOYD-HOARE CALCULUS FOR ITERATION THEORIES 583
8 THE STANDARD EXAMPLE, AGAIN 585
9 COMPLETENESS 586
9.1 THE INVARIANT GUARD PROPERTY 586
9.2 COMPLETENESS OF FLOYD-HOARE RULES 589
9.3 GUARANTEES OF COMPLETENESS 591
9.4 WEAKEST LIBERAL PRECONDITIONS AND COMPLETENESS 594
9.5 THE COOK COMPLETENESS THEOREM 598
9.6 THE UNWINDING PROPERTY 599
10 EXAMPLES 601
10.1 AN EXAMPLE OF A CORRECTNESS PROOF 601
10.2 THE INTERPOLATION PROPERTY DOES NOT IMPLY THE INVARIANT GUARD
PROPERTY 606
10.3 A NON-EXPRESSIVE STRUCTURE WITH WEAKEST LIBERAL PRECONDITIONS 610
11 NOTES 611
LIST OF SYMBOLS 612
INDEX 615
BIBLIOGRAPHY 621
|
| any_adam_object | 1 |
| author | Bloom, Stephen L. Ésik, Zoltán 1951-2016 |
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| ctrlnum | (OCoLC)27640709 (DE-599)BVBBV008188907 |
| dewey-full | 005.13/1 |
| dewey-hundreds | 000 - Computer science, information, general works |
| dewey-ones | 005 - Computer programming, programs, data, security |
| dewey-raw | 005.13/1 |
| dewey-search | 005.13/1 |
| dewey-sort | 15.13 11 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Informatik Mathematik |
| format | Book |
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| indexdate | 2024-07-09T17:16:03Z |
| institution | BVB |
| isbn | 3540563784 0387563784 |
| language | English |
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| spelling | Bloom, Stephen L. Verfasser aut Iteration theories the equational logic of iterative processes Stephen L. Bloom ; Zoltán Ésik Berlin u.a. Springer 1993 XV, 630 S. txt rdacontent n rdamedia nc rdacarrier EATCS monographs on theoretical computer science Literaturverz. S. 621 - 630 Computer science Mathematics Iterative methods (Mathematics) Logic, Symbolic and mathematical Iterationstheorie (DE-588)4027855-4 gnd rswk-swf Fixpunkt Datensicherung (DE-588)4154497-3 gnd rswk-swf Iterationstheorie (DE-588)4027855-4 s DE-604 Fixpunkt Datensicherung (DE-588)4154497-3 s Ésik, Zoltán 1951-2016 Verfasser (DE-588)113300441 aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005405009&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bloom, Stephen L. Ésik, Zoltán 1951-2016 Iteration theories the equational logic of iterative processes Computer science Mathematics Iterative methods (Mathematics) Logic, Symbolic and mathematical Iterationstheorie (DE-588)4027855-4 gnd Fixpunkt Datensicherung (DE-588)4154497-3 gnd |
| subject_GND | (DE-588)4027855-4 (DE-588)4154497-3 |
| title | Iteration theories the equational logic of iterative processes |
| title_auth | Iteration theories the equational logic of iterative processes |
| title_exact_search | Iteration theories the equational logic of iterative processes |
| title_full | Iteration theories the equational logic of iterative processes Stephen L. Bloom ; Zoltán Ésik |
| title_fullStr | Iteration theories the equational logic of iterative processes Stephen L. Bloom ; Zoltán Ésik |
| title_full_unstemmed | Iteration theories the equational logic of iterative processes Stephen L. Bloom ; Zoltán Ésik |
| title_short | Iteration theories |
| title_sort | iteration theories the equational logic of iterative processes |
| title_sub | the equational logic of iterative processes |
| topic | Computer science Mathematics Iterative methods (Mathematics) Logic, Symbolic and mathematical Iterationstheorie (DE-588)4027855-4 gnd Fixpunkt Datensicherung (DE-588)4154497-3 gnd |
| topic_facet | Computer science Mathematics Iterative methods (Mathematics) Logic, Symbolic and mathematical Iterationstheorie Fixpunkt Datensicherung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005405009&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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